Respuesta :
Given:
the perimeter of a rectangle is
[tex]36\text{ cm.}[/tex]The length of the rectangle is 4 cm more than its width.
Required:
We have to find the dimension of the rectangle which is the length and width of the rectangle.
Explanation:
Let the width of the rectangle be
[tex]x\text{ cm.}[/tex]Then the length of the rectangle will be
[tex](x+4)\text{ cm.}[/tex]Now we use the formula for the perimeter of a rectangle to find the required answer.
Then proceed as follows:
[tex]\begin{gathered} 2(\text{ length}+\text{ width\rparen}=36 \\ \Rightarrow2\lbrace(x+4)+x\rbrace=36 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow\lbrace x+4+x\rbrace=\frac{36}{2} \\ \Rightarrow2x+4=18 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow2x=18-4 \\ \Rightarrow2x=14 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow x=\frac{14}{2} \\ \Rightarrow x=7\text{ cm.} \end{gathered}[/tex]Therefore the width of the rectangle is
[tex]7\text{ cm.}[/tex]And the length of the rectangle is
[tex]x+4=7+4=11\text{ cm.}[/tex]Final answer:
Hence the final answer is
[tex]7\text{ cm and }11\text{ cm.}[/tex]